"A big part of the job is going to be over the next couple of years for me is how are we going to reach out to those communities in the way that we've done in Melbourne," he said after being elected leader on Tuesday.

Mr Bandt represents the heart of Melbourne - the city, and the closest, most fashionable, most scruffy suburbs such as north Fitzroy and Richmond. Once a Labor seat, it has shifted relentlessly Green, from an already hefty 36 per cent primary vote in 2010 to 49 per cent last year, the biggest Green vote anywhere.

He said people looked to the Greens not only because of the climate crisis but also the inequality crisis. His seat had the most public housing tenants of any Victorian seat, the highest number of student and big groups of students and young families and some of the poorest people in the state, who, he says, help him hand out how to vote cards.

Bandt believes the Greens can win votes where the Nationals pace in the bush, accusing the Nationals of claiming to champion farmers and people on low incomes but damaging their cause in parliament.

Referring to National leader Michael McCormack's attack on "raving inner-city lunatics" for linking climate change and bushfires, he said Mr McCormack and Prime Minister Scott Morrison were "a good five or 10 years behind where people are at".

In a family sense, Mr Bandt is five or so years behind former leader Richard Di Natale, who quit to spend time with his sons, aged 9 and 11. Mr Bandt's daughters are 4 and 3 and he says he has been in politics since before they were born so they know nothing else. The family lives in Flemington and he makes a point of being home on Sundays to take his girls to swimming lessons, a routine he plans to keep up.

He himself went to primary school in Adelaide, moving to Perth for high school, where he joined the Labor Party, and for university, where he quit the party over student fees. He later became an industrial lawyer, when he had "fought big corporations on behalf of clothing outworkers, and also represented firefighters and even coal workers who were battling with privatisation".

On Tuesday, he put free education as one of his top three priorities. First off, scrapping school fees for public schools. His other priorities are extending Medicare to cover dentistry and a "manufacturing renaissance" based on renewable energy.

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The Greens have mild-mannered leaders, but have also made a brand of the kind of fighty rhetoric epitomised by Bob Brown and most recently also by Senator Di Natale. Mr Bandt is in the same mould - not in the mood to serve up compromise in his first pitch as leader.

"Big business that makes its money by killing people and endangering people's safety should be worried," he said, warning that corporations would be held responsible for climate change and environmental damage.

"If you are a coal company or a gas company or an oil company then our message to you is very simple. Your business model is unsustainable, your business model is predicated on threatening human life, and [you] have to go."

His appeal is to 16 and 17-year-olds who will be at voting age next election, who he says have most to lose from the unequal economy and climate change.

"You are right to feel that you are getting screwed over from every angle as you watch a criminal government burn your future," Mr Bandt said. "But now is not the time for despair. Now is the time to fight back."